1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
|
7-DIMENSIONAL PARTICLE PHYSICS DATA
source: Friedman and Tukey, 1974 "A Projection Pursuit Algorithm for
Exploratory Data Analysis" IEEE Trans. Comput. C, 23, 881-889.
There are 500 observations taken from a high energy particle physics
scattering experiment which yields four particles. The reaction can be
described completely by 7 independent measurements. The important
features of the data are short-lived intermediate reaction stages
which appear as protuberant ``arms'' in the point cloud.
The projection pursuit guided tour is the tool to use to understand
this data set. Using all 7 variables turn on projection pursuit and
optimize with the Holes index until a view is found that has a
triangle and two arms crossing each other off one edge (this is very
clear once you see it but the Holes index has a tendency to get stuck
in another local maximum which doesn't have much structure). Brush the
arms separate colours and glyphs. Change to the Central Mass index and
optimize. As new arms are revealed brush them and continue. When you
have either run out of colours or time turn off projection pursuit and
watch the data touring. Then it becomes clear that the underlying
structure is a triangle with 5 or 6 arms (some appear to be
1-dimensional, some 2-dimensional) extending from the vertices.
|
